lördag 11 augusti 2012

Why the Kutta Trick is Illegal

The accepted text book theory of lift of a wing is based on the Kutta condition requiring the velocity of a 2d (incompressible inviscid) Euler solution to be zero at a trailing edge of positive angle.  But it is mathematically illegal and physically impossible to impose the velocity of an Euler solution to vanish on a part of the boundary and in particular at a single point; the normal velocity can be imposed to be zero on a solid boundary but the tangential velocity cannot be prescribed as a mathematically and physically meaningful boundary condition for an Euler solution. This is acknowledged by referring to the Kutta condition as a "trick".

The violation of mathematical and physical law committed by imposing the Kutta condition is masked by the fact that it is imposed at a singularity of the boundary curve, the sharp trailing edge. The crime committed is thus hidden to inspection under the cover of a singularity, but a clever cop is not fooled by such a simple "trick". Are you?

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